Topology-based Simplification for Feature Extraction from 3D Scalar Fields

Abstract

This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. We present a combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of two atomic operations that removes pairs of critical points. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flows between critical points of a function. Critical points paired by the Morse-Smale complex identify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting desirable features. We also present a visualization of the simplified topology.